10. (a) Derive an expression for the rate constant of a firstorder rea

1.	10. (a) Derive an expression for the rate constant of a firstorder reaction ? How does the rate constant relateto the half life period?(b) Prove that for the first order reaction, the timerequired for 99% completion of the reaction is twicethe time required to complete 90% of the reactions.(C.H.S.E. Instant 2012)
Answer» Let's say rate constant of the first order reaction is 'k'. Time taken for the reaction to process is ‘T’. Half life of the reaction ‘t’. Now the reaction is k={ 2.303×log(a/a-x)}/T Now 'a' is initial concentration to find 't' reaction should proceed to half completion. i.e a/2 take in the place of x When you substitute the values we get k=0.693/T As T=t (half reaction). t=0.693/k It is the half life of the reaction with respect to rate constant k For the log the base should be 'e' thanks

10. (a) Derive an expression for the rate constant of a firstorder reaction ? How does the rate constant relateto the half life period?(b) Prove that for the first order reaction, the timerequired for 99% completion of the reaction is twicethe time required to complete 90% of the reactions.(C.H.S.E. Instant 2012)

Answer»

Let's say rate constant of the first order reaction is 'k'.

Time taken for the reaction to process is ‘T’.

Half life of the reaction ‘t’.

Now the reaction is

k={ 2.303×log(a/a-x)}/T

Now 'a' is initial concentration to find 't' reaction should proceed to half completion.

i.e a/2 take in the place of x

When you substitute the values we get

k=0.693/T

As T=t (half reaction).

t=0.693/k

It is the half life of the reaction with respect to rate constant k

For the log the base should be 'e'

thanks